APSC 174J: Linear Algebra (winter/spring 2010)

Schedule change : Quiz 2 will be during the lecture period on Thursday, May 20, rather than during the tutorial period.

Instructor: Tristram Bogart (JEFF 512)
Email Address: bogart (at) mast.queensu.ca

Schedule

Lectures:

March 1-April 9: Monday 14:30-15:20, Tuesday 16:30-17:20, and Thursday 15:30-16:20 in MCL 315
April 26-30: Monday 11:30-12:20, Tuesday 13:30-14:20, Thursday 11:30-12:20 in MacCorrie B-201.
May 3-June 4: Monday 11:30-12:20, Tuesday 13:30-14:20, Thursday 11:30-12:20 in JEFF 128.

Tutorial:

March 1-April 9: Wednesday 14:30-15:30 in JEFF 128
April 26-30: Thursday 10:30-11:30 in MacCorrie B-201
May 3-June 4: Thursday 10:30-11:30 in JEFF 128

Office Hours:

March 1-April 9: Monday 11:30-12:30 and Tuesday 17:30-18:30 in JEFF 512
April 26-June 4: Monday 12:30-13:30 and Tuesday 14:30-15:30 in JEFF 512.

Materials

Lecture notes for each week will be posted by Thursday's lecture. It is strongly recommended that you read these notes carefully as a complement to the classroom lectures. There will also be regular reading assignments from the textbook Linear Algebra (4th edition) by Friedberg, Insel, and Spence. However, we will cover only selected portions of the textbook, which you should regard as a supplement to the classroom lectures and lecture notes.

Lecture Notes, currently updated through Week 12.

A list of key definitions, theorems, and procdures to know for the final exam.

Homework

To learn almost any part of mathematics, it is essential to spend time solving problems. Accordingly, there will be weekly homework assignments taken from the lecture notes and textbook and posted by the beginning of class on Thursday. Solutions to selected problems in each week's homework will be posted the following week. A solution is not only an answer, but also an explanation. You should read the posted solutions to get an idea of what comprises a complete solution.

Assignments and Solutions

Week 1
- Read Section 1 of the lecture notes available from this page.
- Do problems 1 (parts a,c,e,g,i), 2, 3, 4, 5, 6, 7, 8, and 9 at the end of these lecture notes. Solutions
Week 2
- Read Section 2 of the lecture notes available from this page and section 1.2 and 1.3 in the textbook.
- Do problems 1, 4, 5, 6, 10, 11, 13, 14 (parts d,e,f,g), 15 (parts a,b,c,d), and 16 at the end of these lecture notes. Solutions
Week 3
- Read Section 3 of the lecture notes available from this page and section 1.4 in the textbook.
- Do problems 1 (parts a,b,c,d,i,j,k,l), 2, 3 (parts a,b,c,h,i), 5, and 6 at the end of these lecture notes. Solutions
Week 4
- Read Section 4 of the lecture notes available from this page and section 1.5 in the textbook.
- Do problems 1 (parts a,b,c,d,k,l,m), 3 (parts a,b,c,d,e,f), and 5 (parts a,b,c,d,e,f,m,n,o,p) at the end of these lecture notes. Solutions
Week 5
- Read Section 5 of the lecture notes available from this page and sections 3.1 and 3.3 in the textbook.
- Do problems 1, 2, 3, 5, 6, 7, 9, and 11 at the end of these lecture notes. Solutions
Week 6
- Read Section 6 of the lecture notes available from this page and section 1.6 in the textbook.
- Do problems 1 (parts a,c,e,g,i,k,m), 2 (parts a,c,e,g,i,k), and 4 (parts a,c,e,f,g,h,i,j,k,n,o,p) at the end of these lecture notes. Solutions
Week 7
- Read Section 7 of the lecture notes available from this page.
- Do problems 4,5,8,11,13,15,22,23, and 24 at the end of these lecture notes. Solutions
Week 8
- Read Section 8 of the lecture notes available from this page and section 2.1 in the textbook.
- Do problems 1 (parts a,b,c,f,g,h,i,j,q,s,u,w), 2, 3, and 4 at the end of these lecture notes. Solutions
Week 9
- Read Section 9 of the lecture notes available from this page and section 2.2 in the textbook.
- Do problem 1 (parts c,d,e,f,j,k,m,n) at the end of these lecture notes. Solutions
Week 10
- Read Section 10 of the lecture notes available from this page and section 2.3 in the textbook.
- Do problem 1 (parts a,b,c,g,h,n,o,v,w,z) at the end of these lecture notes. Solutions
Week 11
- Read Section 11 of the lecture notes available from this page and sections 4.1, 4.2, and 4.3 in the textbook.
- Do problems 1 (parts a,b,c), 2, 3, 4, and 5 (parts a,b,e,f,j,k,n,q,t,u,x,y) at the end of these lecture notes. Solutions
Week 12
- Read Section 12 of the lecture notes available from this page and section 5.1 in the textbook.
- Do problems 1 (parts a,b,c,d,e,l,m,s,t,u,v,w,x,y), 2, 3, and 4 at the end of these lecture notes. Solutions

Exams

There will be two quizzes, a midterm, and a final exam. The first quiz will occur during the lecture period on Thursday, March 18, the midterm during lecture on Thursday, April 8, and the second quiz during lecture on Thursday, May 20. The final exam will occur between June 7 and June 11, with exact date and time to be determined. Update: The final exam will take place on June 8, at 2:00 pm in WLH 205. Only calculators with gold stickers are allowed; however, no question will be designed to require the use of a calculator. Here are the solutions to Quiz 1 and the solutions to Quiz 2.

Marking Scheme

Quiz 1	10%
Midterm	25%
Quiz 2	10%
Final exam	55%

Disabilities

Students with disabilities who will be taking this course and may need disability-related classroom accommodations are encouraged to make an appointment to see the instructor as soon as possible. Also, stop by the Health, Counseling and Disability Services Office to register for support services.

Academic Integrity

It is the obligation of each student to understand the University's policies regarding academic honesty and to uphold these standards. Students are encouraged to talk about the problems, but should write up the solutions individually. Students should acknowledge the assistance of any books, software, students or professors. In that spirit:

Approximate Lecture Schedule

(updated May 20)

Week	Dates	Topic
1	March 1-5	Introduction to linear systems; review logic, sets, and functions
2	March 8-12	Vector spaces and subspaces
3	March 15-19	Subspaces, linear combinations, linear span; Quiz 1
4	March 22-26	Linear dependence and independence
5	March 29-April 2	Solving systems of linear equations
6	April 5-9	Generating sets, bases, and dimension of a vector space; Midterm
7	April 26-30	Linear transformations
8	May 3-7	Matrices and linear transformations
9	May 10-14	Kernels, images, and the rank-nullity theorem
10	May 17-21	Application to solving linear systems; matrix multiplication; Quiz 2
11	May 24-28	Inverses and invertibility
12	May 31-June 4	Eigenvalues and eigenvectors